Cambridge International AS and A Level Mathematics Pure Mathematics 1

Answers 292 P1^ 9 (i) f(x)  2 (ii) k = 13 10 (i) k = 4 or −8; x = 1 or − 5 (ii)  7 (iii)  92 – xx, x ≠ 0 11 (i) 2(x − 2)^2 + 3 ...

Chapter (^5) 293 P1^ 31 8 x − 1 32 4 x + 5 33 1 34 16 x^3 − 10 x (^35 32) (^12) x 36 1 x 37 92 x −^1 x 38 34 x^2 −^12 x + 4 39 3 ...

Answers 294 P1^ 10 (i) ddyx = −^720 x (ii) 0.8225 and −0.8225 (iii) x=^107 11 (i) (ii) (−^12 , 0) (iii) − x^12 (iv) − 4 12 (i) − ...

Chapter (^5) P1^ (ii) At (1, 0), ddyx = − 1 At (2, 0), d d y x = 1 (iii) At (1, 0), tangent is y = −x + 1, normal is y = x − 1 A ...

Answers 296 P1^   7 (i) ddyx = 3(x + 3)(x − 1) (ii) x = −3 or 1 (v)   8 (i) ddyx = −3(x + 1)(x − 3) (ii) Minimum when x = −1, ma ...

Chapter (^5) 297 P1^ (vi) (1, 2), minimum and (−1, −2), maximum (vii) (^) ( 12 , 12) , minimum (viii) ( 2 , 8 2 ) , minimum and ...

Answers P1^ d d h t^ is the rate of change of the height of the sand with respect to time. d d d d V h h × t is the rate of chan ...

Chapter (^6) 299 P1^ 15 y = 6 x − x 2 2 +^2 16 (i) y = 4 x − 12 x^2 + 3 (ii) x + 2 y = 20 (iii) (7, 6.5) Activity 6.1 (Page 183) ...

Answers 300 P1^ (ii) (^113) (iii) (iv) (^113) (v) The answers are the same, since the second area is a translation of the first. ...

Chapter (^6) P1^ (vii) 1 6 square units (viii) 816 square units (ix) 11121 square units (x) 816 square units 2 (i) (^) ddyx = 20 ...

Answers 302 P1^ 11  4.5 square units 12 (i) ddyx = 6 x − 6 x^2 − 4 x^3 (ii) 4 x + y − 4 = 0 (iv) 8.1 square units 13 (i) ddyx = ...

Chapter (^7) ● P1 ? (Page 209)   1 (i) A cylinder (ii) A sphere (iii) A torus   2 73 π ●^ (Page^ 211) Follow the same procedure ...

Answers P1^   4  (i) 89 3   5  (i)  4 d   6  (i) BX =  33 Activity 7.1 (Page 223) ●?^ (Page^ 227)   1 The oscillations continue ...

Chapter (^7) 305 P1^ (vii) (^12) (viii) 23 (ix) − 1   5 (i) −60° (ii) −155.9° (iii) 54.0°   6 (i) (ii) (a) False (b) True (c) Fa ...

Answers 306 P1^   2 (i) (a)  203  cm^2 (c) 16.9 cm^2 (ii) 19.7 cm^2   3 (i) 1.98 mm^2 (ii) 43.0 mm   5 (i) 140 yards (ii) 5585 ...

Chapter (^8) 307 P1^ (iv) (a) (b) y = sin x (v) (a) (b) y = −cos x   4 (i) y = tan x + 4 (ii) y = tan (x + 30°) (iii) y = tan (0 ...

Answers 308 P1^ Start with the vector OQ→ = a 1 i + a 2 j. Length = aa 12 + 22 Now look at the triangle OQP. OP^2 = OQ^2 + QP^2 ...

Chapter (^8) P1^ 4  (i) (a) i (b) 2 i (c) i − j (d) −i − 2 j (ii) | A → B | = | B → C | = 2 , | A → D | = | C → D | = 5 5  ( ...

Achilles and the tortoise 94 addition of vectors 263–4 see also sum; summation algebraic expressions, manipulating 1 angles betw ...

Index P1^ formula binomial coefficients 97–9 changing the subject 10–11 definition 10 for momentum after an impulse 11 quadratic ...